This article presents a unifying classification for functional regression modeling, and more specifically for modeling the link between two variables X and Y, when the explanatory variable (X) is of a functional nature. It first provides a background on the proposed classification of regression models, focusing on the regression problem and defining parametric, semiparametric, and nonparametric models, and explains how semiparametric modeling can be interpreted in terms of dimension reduction. It then gives four examples of functional regression models, namely: functional linear regression model, additive functional regression model, smooth nonparametric functional model, and single functional index model. It also considers a number of new models, directly adapted to functional variables from the existing standard multivariate literature.
Flexible variable selection for recovering sparsity in nonadditive nonparametric models
